Quadrilateral opqr is inscribed in circle n, as shown below. which of the following could be used to calculate the measure of ∠opq? circle n is shown with a quadrilateral opqr inscribed inside it. angle o is labeled x plus 16. angle p is not labeled. angle q is labeled 6x minus 4. angle r is labeled 2x plus 16.

answer choices
∠opq + (2x + 16)° = 180°
m∠opq = (6x − 4)° + (2x + 16)°
m∠opq + (x + 16)° + (6x − 4)°= 360°
m∠opq = (x + 16)° + (6x − 4)°

first option.

Step-by-step explanation:

By definition, the sum of opposite angles in a quadrilateral inscribed in a circle is 180°.

Observe the figure.

You can notice that the angle   and the angle are opposite, which means that they sum is 180°.

Knowing this, you can write the following equation:

Based on the figure, you know that:

Therefore, substituting this into the equation ,  you get the following equation that can be used to calculate the measure of :

answer: x=3 and y=4

step-by-step explanation: